SEMICONDUCTORS AND SEMIMETALS pot

In Chapter 2, Carlson reviews and compares various a-Si : H deposition methods that have been used to make solar cells.. He points out the impor- tance of various material properties to

Semiconductors and Semimetals

RCAfDAVlD SARNOFF RESEARCH CENTER

PRINCETON NEW JERSEY

1984

Harcourt Brace Jovanovich, Publishers

Orlando San Diego New York

Austin London Montreal Sydney

Tokyo Toronto

COPYRIGHT @ 1984, BY ACADEMIC PRESS, INC

ALL RIGHTS RESERVED

NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN A NY FORM OR BY A N Y MEANS, ELECTRONIC

OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR Am

INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT

PERMISSION IN WRITING FROM THE PUBLISHER

ACADEMIC P R E S S , INC

Orlando, Florida 32887

United Kingdom Edition published by

ACADEMIC PRESS, INC (LONDON) LTD

24/28 Oval Road, London NWl IDX

Library of Congress Cataloging in Publication Data

(Revised for volume 2 18-21 D)

Main entry under title:

Semiconductors and semimetals

Includes bibliographical references and indexes

Contents: v 1-2 Physics of 111-V compounds v 3 Optical properties of Ill-V compounds

pt B, C, D Hydrogenated amorphous silicon

Collected works I Willardson, Robert K 11 Beer,

Contents

LIST OF CONTRIBUTORS xi

FOREWORD xiii

PREFACE xv

Chapter 1 Introduction Jacques I Pankove 1 References 6

Chapter 2 Solar Cells D E Carlson I Introduction 7

I1 MethodsofGrowing AmorphousSilicon for Solar Cells 8

I11 Relevant Material Properties 10

IV Solar-Cell Fabrication and Performance 19

V Cost Projections 32

VI Future Directions 33

References 35

Chapter 3 Closed-Form Solution of I - Y Characteristic for a-Si : H Solar Cells G A Swartz List of Symbols 39

I Introduction 40

I1 ProposedModel 40

111 Interrelation of q FF and JJJ, 49

IV Summary 52

References 53

V

vi CONTENTS

Chapter 4 Electrophotography

Isamu Shimizu

I Introduction 55

I1 Advantages Expected from a-Si : H as Photoreceptor of Electrophotography 56

I11 Material Design for a-Si : H Photoreceptor 58

IV Photoinduced-Discharge (PID) Characteristics 62

V Problems Remaining Today 72

References 72

Chapter 5 Image Pickup Tubes Sach io Ish ioka I Introduction 75

I1 a-Si: H Image Pickup Tube 76

I11 Properties of a-Si : H 78

IV Blocking Contact Structure of the Photoconductive Target 80

V Impurity Doping of a-Si : H 82

VI Characteristics of a-Si : H Image Pickup Tubes 83

VII Applications for a-Si : H Target 86

References 87

Chapter 6 The Development of the a-Si : H Field-Effect Transistor and Its Possible Applications P G LeComber and W E Spear I Introduction

I1 The Field Effect in Glow-Discharge a-Si : H I11 Design and Fabrication of the a-Si : H FET IV Direct-CurrentCharacteristics

V DynamicPerformance

VI Reproducibility and Stability

VII Investigation of the ON-State

VIII Radiation Hardness of a-Si : H FETs IX Some Possible Applications of a-Si : H FETs X Limitations of Present a-Si : H FETs References

89

90

93

95

98

99

101

105

108

112

113

Chapter 7 a-Si : H FET-Addressed LCD Panel D G Ast I Introduction 115

I1 Properties of Liquid Crystals 115

CONTENTS vii

I11 Principles of Multiplexing

IV Electrical Specifications of Extrinsic Threshold Devices

V Active-Matrix-Addressed Liquid Crystal Displays

Chapter 8 Solid-state Image Sensor S Kaneko I Introduction 139

I1 Application to a Long Linear Image Sensor 140

I11 Application to a Scanning Circuit 152

154

V Future Expectations 157

References 157

IV Application to an Area Image Sensor Chapter 9 Charge-Coupled Devices Masakiyo Matsumura I Introduction 161

I1 Theoretical Results on Charge Transfer 162

111 CCD Structure for High-Frequency Operation 167

IV Experimental Results 168

References 172

V Conclusion 171

Chapter 10 Optical Recording M A Bosch I Summary 173

I1 Introduction and Scope 174

111 Optical Recording in a-Si 175

IV Optical Recording in a-Si : H 183

V Electrically Amplified Writing 199

VI Outlook 205

References 206

Chapter 1 1 Ambient Sensors A D’Amico and G Fortunato 1 I n t r o d u c t i o n 209

I1 Adsorbate Effects 211

viii C 0 N T E N T S

I11 Thermistors 213

IV MIS Diodes for Hydrogen Detection 216

V FET Structures for Ion and Gas Sensors 228

VI Conclusions 234

References 235

Chapter I 2 Amorphous Light-Emitting Devices Hiroshi Kukimoto I Introduction 239

241

111 Electroluminescence of a.Si.C,- : H 244

IV Future Developments 245

References 247

I1 Preparation and Properties of a.Si.C,- H Chapter 13 Fast Detectors and Modulators Robert J Phelan Jr I Introduction 249

I1 Devices 251

111 Conclusions 258

References 259

Chapter 14 Hybrid Structures Jacques I Pankove 1 Introduction 261

I1 Passivation of Crystalline Silicon 261

111 Heterojunctions 270

IV Optical Waveguides 272

References 272

Chapter 15 Electronic Switching in Amorphous Silicon Junction Devices P G LeComber A E Owen W E Spear J Hajto and W K Choi I Introduction 275

I1 Previous Work on Electrical Switching in Amorphous Silicon 277

111 Device Structure and Fabrication 279

CONTENTS ix

IV Static Current-Voltage Characteristics of Virgin Devices

V Forming: Static Characteristics

VI Forming: Dynamic Characteristics

VII Dynamic Switching of Formed Devices

VIII Discussion of Possible Switching Mechanisms

279

.281

.282

284

286

References 288

INDEX

CONTENTSOFPREVIOUSVOLUMES . . . .

291 295

This Page Intentionally Left Blank

List of Contributors

Numbers in parentheses indicate the pages on which thi: authors’ contributions begin

D G Asr, Department of Materials Scietice and Engineering, Cornell

M A BOSCH, AT&T Bell Laboratories, Holmdel, New Jersey 07733 (173)

D E CARLSON,* RCA/David Sarnof Restparch Center, Princeton, New Jersey 08540 (7)

W K C H O I , Department of Electrical Engineering, University of Edin-

burgh, Edinburgh EH9 3JL, Scotland (275)

A D’AMICO, Istituto di Elettronica dell0 Star o Solido, Consiglio Nazionale

delle Ricerche, 00156 Rome, Italy (209)

G FORTUNATO, Istituto di Elettronica delh Stato Solido, Consiglio Na-

zionale delle Ricerche, 00156 Rome, Italy (209)

J HAJTO, Department of Electrical Engineering, University of Edinburgh,

Edinburgh EH9 3JL, Scotland (275)

SACHIO ISHIOKA, Central Research Laborat wy, Hitachi, Ltd., Kokubunji,

Tokyo 185, Japan (75)

S KA N E KO, Microelectronic Research Lat lorat ories, NEC Corporation,

Kawasaki 213, Japan (1 39)

HIROSHI KUKIMOTO, Imaging Science and Engineering Laboratory, Tokyo

Institute of Technology, Nagatsuta, Yokohama 227, Japan (239)

P G LECOMBER, Carnegie Laboratory of P)hysics, The University of Dun-

dee, Dundee DDI 4HN, Scotland (89, 275)

MASAKIYO M A r S u M u R A , Department of Physical Electronics, Tokyo Insti-

tute of Technology, 0-Oka.yama, Tokyo 152, Japan (16 1 )

A E O W E N , Department of Electrical Enpineering, University of Edin-

burgh, Edinburgh EH9 3JL, Scotland (275)

JACQUES I PANKOVE, RCA/David Sarnoj- Research Center, Princeton, New Jersey 08540 ( 1 , 26 1 )

University, Ithaca, New York 14853 ( 1 15)

* Present address: Thin Film Division, Solarex Cxporation, Newtown, Pennsylvania

18940

xi

xii LIST OF CONTRIBUTORS

ROBERT J PHELAN, JR., National Bureau of Standards, Boulder, Colorado

ISAMU S H I M I Z U , Imaging Science and Engineering Laboratory, Tokyo

W E SPEAR, Carnegie Laboratory of Physics, The University of Dundee,

G A SWARTZ, RCA/David SarnoflResearch Center, Princeton, New Jersey

80303 (249)

Institute of Technology, Nagatsuta, Yokohama 227, Japan (55)

08540 (39)

Foreword

This book represents a departure from the usual format of “Semiconduc- tors and Semimetals” because it is a part of a four-volume miniseries devoted entirely to hydrogenated amorphous silicon (a-Si : H) In addition, this group of books - Parts A - D of Volume 2 1 -has been organized by a

guest editor, Dr J I Pankove, an internatiorially recognized authority on

this subject He has assembled most of the who’s who in this field as authors

of the many chapters It is especially fortunate that Dr Pankove, who has made important original contributions to our understanding of a-Si : H, has been able to devote the time and effort necessary to produce this valuable addition to our series In the past decade, a-Si : H has developed into an important family of semiconductors In hydrogenated amorphous silicon alloys with germanium, the energy gap decreases with increasing germa- nium content, while in alloys with increasing carbon content the energy gap increases Although many applications are still under development, efficient solar cells for calculators have been commercial for some time

In Volume 21, Part A, the preparation of a-Si:H by rf and dc glow discharges, sputtering, ion-cluster beam, CVD, and homo-CVD techniques

is discussed along with the characteristics of the silane plasma and the resultant atomic and electronic structure and characteristics

The optical properties of this new family of semiconductors are the subject of Volume 2 1, Part B Phenomena discussed include the absorption

edge, defect states, vibrational spectra, electroreflectance and electroabsorp- tion, Raman scattering, luminescence, photoconductivity, photoemission, relaxation processes, and metastable effects

Volume 2 1, Part C, is concerned with electronic and transport properties, including investigative techniques employing field effect, capacitance and deep level transient spectroscopy, nuclear and optically detected magnetic resonance, and electron spin resonance Parameters and phenomena con- sidered include electron densities, carrier mobilities and diffusion lengths, densities of states, surface effects, and the Staebler- Wronski effect The last volume of this miniseries, 2 1, Part 13, covers device applications, including solar cells, electrophotography, im.sge pickup tubes, field effect transistors (FETs) and FET-addressed liquid crystal display panels, solid

state image sensors, charge-coupled devices, optical recording, visible light

xiii

xiv FOREWORD

emitting diodes, fast modulators and detectors, hybrid structures, and memory switching

R K WILLARDSON ALBERT C BEER

Preface

Hydrogenated amorphous silicon, a new form of a common element, is a semiconductor that has come of age Its scientific attractions include a continuously adjustable band gap, a usable camer lifetime and diffusion

or p-type dopants

Furthermore, it can be fabricated very easily as a thin film by a technology that not only inherently escapes the expenst: of crystal perfection but also requires significantly smaller amounts of raw materials

The discovery of a new material endowed with wondrous possibilities for very economical practical applications naturally attracts many researchers who invariably provide new insights and further vision Their meditation and experimentation build up rapidly and lead to a prolific information flow

in journals and conference proceedings

The initial cross-fertilization generates an overload of data; books are written that attempt to digest specialized aspects of the field with state-of- the-art knowledge that often becomes obsolete by the time the books are published a year or two later

We have attempted to provide this book with a lasting quality by empha-

the properties of hydrogenated amorphous silicon but also how and why they are measured, and the variety of practical applications possible with this method

In most chapters, a brief historical review depicts the evolution of relevant concepts The state of the art emerges, and a bridge to future developments guides the reader toward what still needs to be done The abundant refer- ences should be a valuable resource for the future specialist

We hope that this tutorial approach by seaslmed experts satisfies the needs

of at least one generation of new researchers

xv

This Page Intentionally Left Blank

SEMICONDUCTORS AND SEMIMETALS VOL 21, PART D

C H A P T E R 1

Introduction

Jacques I Pankove

R C A ~ D A V I D SARNOFF RESEARCH CENTER

PRINCETON, NEW JERSEY

This first chapter summarizes the content:; of this volume Where rele- vant, we have added several other new device applications of a-Si : H that have come to our attention since the authors have written their contribu- tions The authors of this volume have belzn chosen for their eminent contributions in the various approaches that 'broaden the usefulness of this material

In Chapter 2, Carlson reviews and compares various a-Si : H deposition methods that have been used to make solar cells He points out the impor- tance of various material properties to the efficient performance of solar cells, for example, the absorption edge that depends on hydrogen concen- tration Also, alloying Si with other elements such as carbon and germanium affects the absorption edge, thus allowing a stacking of cells with successively narrower energy band gaps to utilize more efficiently the solar spectrum Carlson discusses the relationship between the collection length and the diffusion length He stresses the detrimental influence of gap states, those due to dangling bonds and those introduced by various impurities that are often present in a deposition system There is also concern for defects that may enhance light-induced effects and concern over the doping efficiency that determines the maximum obtainable photovoltage Several cell struc- tures are described and the performance of the better cells is reported Light-induced degradation is negligible in thin cells because the resulting large electric field separates the photogenerated electron - hole pairs before they can recombine Carlson describes techniques for making solar cells on a commercial scale He considers the economics of solar-cell fabrication for power generation (e.g., most of the cost is in the supporting structure) and projects that a 20% conversion efficiency using stacked cells could be achieved by the end of this decade

In Chapter 3, Swartz presents a model for tliep- i-n solar cell consisting

of two transitions (like two portions of a p - n junction) separated by a

photoconductive i layer Various physical properties can be incorporated

1

Copyright 0 1984 by Academic Prrss Inc

AU rights of mroduction in any form mrved

2 JACQUES I PANKOVE

into the lumped-circuit constants to generate the corresponding I - V char- acteristics Conversely, the observed characteristic can be used to evaluate the appropriate physical property Thus, the light-induced degradation can

be attributed to a reduced bamer at the p+-i layer interface and to a

reduction of the pct product

In Chapter 4, Shimizu describes the use of a-Si : H as a photoreceptor for transferring an image by electrophotography Hydrogenated amorphous silicon is endowed with a very low electrical conductivity, a long charge decay time, an excellent spectral sensitivity in the visible, and a good chemical inertness The retention of a surface charge is helped by blocking layers at both surfaces of the a-Si : H films An excellent image reproducibil- ity with high resolution and good contrast was demonstrated in a commer- cial machine whose Se-coated drum was replaced by one coated with a-Si : H

Hydrogenated amorphous silicon photoreceptors for electrophotography have been coated with a thin layer (< 100 nm) of a-SiO, : H by Nakayama ef

al ( 1983) This overcoat improves the stability of the photoreceptor against

temperature and humidity cycling A photoreceptor consisting of a 1-pm-

thick layer of a-SiGe : H sandwiched between two a-Si : H layers was devel-

oped by Nishikawa et al ( 1983) to match a GaAlAs LED This device, which has a sensitivity of 0.5 pJ cm-, at 600 nm, was passivated with a thin layer

of a-Sic

In Chapter 5, Ishioka describes the use of a-Si : H in imaging tubes The a-Si: H is a photoconductor having the vacuum side charged to cathode potential Light causes charge leakage during a frame time; the signal is the electron-beam current needed to recharge the surface Blocking contacts are used to reduce the leakage current Hydrogenated amorphous silicon has a broad spectral response that is especially sensitive in the visible range The signal current is proportional to the light intensity at all wavelengths, which simplifies color balancing The spatial resolution is comparable to that of commercial vidicons and exhibits neither blooming nor image burning under strong illumination When used to intensify x-ray images, the a-Si : H

imaging tube has a better resolution than conventional image intensifiers A single-tube color camera has been demonstrated using striped color filters

on the face plate

Although the development of field-effect transistors (FETs) has already reached a high level of perfection in crystalline silicon (c-Si), a-Si : H offers the advantage that very large arrays of a-Si : H FETs are feasible Hence, even if their performance level is much lower than that of c-Si FETs, there are still many applications where their characteristics may be adequate In Chapter 6, LeComber and Spear review the design, fabrication, and per- formance of a-Si : H FETs They point out the need for good ohmic connec-

1 INTRODUCTION 3

tions to source and drain and the problem of achieving a good dielectric under the gate Sheet conductance of several lo-* m h o n and switching times on the order of a microsecond have been obtained These devices appear very resistant to gamma radiation Among applications briefly discussed are inverter logic and addressable image sensors The figure of merit given by the gain - bandwidth product is 5 MHz, a limitation that still

allows many practical uses

In Chapter 7, Ast describes the application of a-Si : H FETs to a liquid crystal display (LCD) There is a brief introdusstory review of the principles involved in changing the orientation of light-polarizing liquid crystals lead- ing to the possibility for high-contrast imaging using either transmitted or scattered light Ast considers the problem of addressing the numerous elements of an LCD, especially when one needs to avoid a dc bias that might degrade the liquid crystals by electrolytic acrion Hence the driving bias must be periodically reversed Thus, a symmetrical back-to-back pair of Schottky diodes could be used to switch liquid crystals allowing several hundred lines of 1-mm-square pixels to be addressed If a high-mobility semiconductor were used, electrical considerations would require that the drivers be made at the limits of lithographic resolution In contrast, the low-mobility a-Si : H is ideally suited for makmg large FETs having a high OFF-resistance Furthermore, a-Si : H has the advantage of low-temperature processing so that it can be deposited onto inexpensive soda-lime glass that serves as a transparent substrate An experimental structure is described that uses a square FET in which the gate surrounds a square drain electrode This drain serves as a large reflecting electrode for the liquid crystal The source electrode that surrounds the gate is an extension of the gate Hence, there is

no need to etch the a-Si : H between source and drain The early model consisting of a 26 X 26 array has been operated for more than one year without degradation

In Chapter 8, Kaneko reviews various image sensors suitable for facsimile transmission or for optical character recognition He then describes a new image sensor consisting of a long array of a-Si : H photocells that sense the light reflected along a line illuminated by it linear array of LEDs An integrated circuit scans the information stored in the photosensors while the array scans a page one line at a time Hydrogenated amorphous silicon is more suitable as a photoconductor for this application than other materials because of its flatter response in the visible spectrum and because the fabrication of a long array is readily feasible Various structures have been explored One that is particularly successful in reducing the dark current employs blocking layers of Si3N, and ptype a-Si : W Several methods of switching from element to element are considered, such as sequential switching with FETs of various types and even using charge-coupled devices

4 JACQUES I PANKOVE

(CCD) It is expected that a superposition of the a-Si : H sensor and a CCD should produce a performance comparable to that of a vidicon With the addition of a laminated color filter comprising lines of red-, green-, and blue-pass filters, a color image sensor was demonstrated

Another potential image sensor is the CCD discussed in Chapter 9 by Matsumura The major problem in using a-Si : H for CCD applications is the high density of traps or localized states in the band gap A theoretical analysis assuming an exponential distribution of gap states permits us to predict the transfer characteristics (residual electron density as a function of time) With state-of-the-art material it should be possible to make usable image sensors Early experimental results with novel test structures have yielded transfer inefficiencies of less than 1 % at clock frequencies between 1 and 200 kHz

In Chapter 10, Bosch reviews optical recording methods, especially those involving a-Si : H There is the possibility of generating a microstructure that has a high absorption coefficient (low reflectance) but becomes highly reflective upon melting by a laser beam, the surface tension helping the formation of a smooth imprint A localized amorphous-to-crystalline phase change also provides absorption and reflectance contrast The most useful result is derived from the thermal dehydrogenation of a-Si : H Dehydrogen- ation provides a decrease in energy gap and hydrogen evolution The latter can form a microscopic blister or a crater that can be easily read optically against a smooth background Bosch describes a system that greatly reduces the laser power required to record data In this approach the a-Si : H is used

as a photoconductor supporting an externally applied voltage The writing energy comes from the electrical power dissipated as heat when the photo- conductor is triggered into conduction by the laser pulse This heat can blister or crater either the photoconductor or an outer layer of a more thermally sensitive material Thus, with an applied voltage, 1.8-pm dots were recorded with 0.1 mW of laser power (two orders of magnitude lower than without applied voltage) The presence of hydrogen that passivates the dangling bonds renders the material corrosion resistant, a quality that is valued for archival information storage

In Chapter 1 1, D’Amico and Fortunato report on the use of a-Si : H for measuring the hydrogen concentration in the ambient and also for measur- ing the temperature of the ambient In the latter application, the a-Si : H is used as a thermistor Hydrogen detection utilizes a field-effect transistor in the form of a MISFET in which a palladium gate catalyzes the H2 dissocia- tion and allows atomic hydrogen to modulate the conductivity of the a-Si : H They also describe MIS sensors in which the hydrogen concentra-

tion is obtained from the C- V characteristics For practical applications,

there is concern over possible long-term changes in barrier height and a need

it is in phosphors) However, our own feeling is that impact excitation may create dangling bonds that would reduce the luminescence efficiency This fear is based on our observation that a-Si : H never exhibited cathodolumi- nescence and on our observation of electron-beam-induced defects (see Volume 2 1 B, Chapter 1 1)

In Chapter 13 Phelan shows that a-Si : H can be used for fast detectors that take advantage of the high absorption coefficient of this material and of the short transit time of photogenerated camers in very small structures in the presence of an electric field Response times in the tens of picoseconds have been obtained Another application for a-Si:H is as a fast electro-optic modulator There, the electric field changes the refractive index and shifts the absorption edge (Franz - Keldysh effect) The change in refractive index

in the film causes a large spectral shift of the interference pattern This change results in a large and rapid modulation of a transmitted monochro- matic light

In Chapter 14 Pankove describes several uses for a-Si : H deposited on crystalline Si The most studied of these aplplications is as a passivating encapsulant that takes advantage of the abundant hydrogen to tie the dangling bonds at the surface of c-Si and provides a reservoir of hydrogen that ensures the stability of the interface Another potential application is as

a heterojunction to make efficient emitters in bipolar c-Si transistors Although several attempts have been made at realizing this structure, no beneficial result has been demonstrated thus far Still another possible hybrid combination of amorphous and crystalline materials is the use of a-Si : H as a waveguide to transfer optical signals over a crystalline integrated circuit without cross talk between optical and electronic interconnections This application, which capitalizes on the high refractive index of a-Si : H, also has not been demonstrated

In Chapter 15, LeComber et al describe an intriguing switching phenom- enon that may have extensive practical applications The device is a diode that can be switched to the conducting state by biasing beyond a threshold

6 JACQUES I PANKOVE

with one polarity and switched back to the resistive state by exceeding a threshold with opposite polarity The switching is fast (- 10 nsec), weakly dependent on temperature, and independent of illumination The diode remains indefinitely in the ON or OFF state until the appropriate threshold

is exceeded

REFERENCES

Nakayama, Y., Wakita, K., Nakano, M., and Kawamura, T (1983) J Non-Cryst Solids

Nishikawa, S., Hakinuma, H., Watanabe, T., and Kaminishi, K (1983) J Non-Crysf Solids

59/60, 1231

59/60, 1235

C H A P T E R 2

Solar Cells

D E Carlsont

RCAfDAVID SARNOFF RESEARCH CENTER

PRINCETON, NEW JERSEY

11 METHODS OF GROWING AMORPHOUS SILICON FOR SOLAR

to 2.4% (Carlson and Wronski, 1976), and in 1977 an efficiency of 5.5% was obtained in a small (2-mm2) Schottky-bamer device (Carlson, 1977b) At about this time, it was becoming clear that hydrogen was playing an important role in assuring the good semiconducting properties of amor-

t Present address: Thin Film Division, Solarex C o r p o r a t i o n , N e w t o w n , P e n n s y l v a n i a

7

Copyright 0 1984 by Academic Rns, Inc

AU rinbts of mroduction in form

metal - insulator- semiconductor (MIS) device fabricated from a glow dis- charge in SiF, and H, (Madan et al., 1980); the film used in this MIS device was a silicon - hydrogen - fluorine alloy (a-Si : H : F)

In 1981 an efficiency of 7.5% was obtained for a p - i - n structure

(3.3 mm2) in which the p layer was a boron-doped silicon-carbon-hydro-

gen alloy (a-Si:C:H) (Tawada et al., 1981) A further improvement in conversion efficiency to 8.5% was obtained in 1982 with a stacked junction structure (9 mm2) that utilized an amorphous silicon-germanium - hydro- gen alloy (a-Si : Ge : H) in the back junction of three stacked p- i - n junc- tions (Nakamura et al., 1982) More recently, an efficiency of 10.1% has

been achieved in a p - i - n structure ( 1.2 cm2) utilizingptype a-Si : C : H as a

window layer (Catalano et al., 1982)

Commercialization of amorphous silicon solar cells started in 1980 when Sanyo introduced calculators powered only by small solar-cell panels (total area - 5 cm2) Shortly thereafter, Fuji Electric also started producing a-Si : H solar cells for calculators As of 1983, a-Si:H photovoltaic devices are produced for several other applications such as photodetectors, power supplies for watches, and NiCd battery chargers Before the end of 1984 one may see a-Si : H solar panels used in larger-scale applications such as imga- tion and remote electrification

In this article, we first review the methods of growing amorphous silicon for solar cells The next part covers the material properties that are relevant

to the development of efficient, stable a-Si : H solar cells In Part IV, we discuss the fabrication, performance, and scale-up of a-Si : H solar cells, and

in Part V, we consider the economics of these cells for various applications

We conclude with some projections for the future of a-Si : H photovoltaics

11 Methods of Growing Amorphous Silicon for Solar Cells

Several techniques have been used to grow a-Si : H films for solar cells As shown in Table I, the highest-efficiency cells have been made from films grown in glow discharges in silane (SiH,) Conversion efficiencies greater than 9% have been reported for devices made from silane glow discharges using rf external capacitive coupling (Hamakawa et al., 1983), rf internal capacitive coupling (Kuwano et al., 1983), and the dc proximity mode (Catalano et al., 1982) Comparable performance has also been reported for devices that were apparently made from glow discharges in silicon tetrafluo- ride (SiF,) and hydrogen (Hack and Shur, 1982) Glow discharges in disilane

2 SOLAR CELLS 9

TABLE I SOLAR-CELL EFFICIENCIES FOR VARIOUS GROWTH TECHNIQUES

Deposition technique Solar-cell structure ?I(%) Reference Glow discharge in Glass/SnO,/p* i- nlAg 10.1 Catalano et al., 1982 SiH,

Sputtering in Ar and ITO/p-i-nlsteel 4.0 Moustakas and

CVD-higher silanes ITO/n-i-pln-i-pln-i-plsteel 4.0 Dalal, 1982

Photo-CVD with Hg glass/ITO/Sn02/p*-i-n/metal 4.39 Inone et al., 1983 CVD-SiH, + posthy- F’t/i-n/n+Sixb 2.7 Hirose, 1981

drogenation

p* is ptype a-Si : C : H

Six is crystalline silicon

(Si2H,) have also been used to make a-Si:H solar cells, but the best efficiency to date is - 8.1% (A W Catalano, private communication, 1983)

Detailed descriptions of the rf and dc glow-discharge deposition tech- niques are presented by Hirose and Uchida in Volume 21A, Chapters 2

and 3

There are some general considerations that pertain to all glow-discharge systems that are used to make solar cells The substrate temperature during film growth is usually in the range of 200-300°C Polymer formation (SiH,), generates defects at lower substrate temperatures (Knights et al.,

1979), and hydrogen out-diffusion creates dangling bonds at higher sub- strate temperatures (Pankove and Carlson, 1977) The power density during deposition cannot be too high since energetic ions and neutrals can damage the growing film (Carlson and Magee, 1979) Power densities are typically less than 0.1 W cm-2 for most glow-discharge deposition systems Also, all discharge systems must be relatively clean and free of air leaks since impurities can reduce the conversion efficiency of solar cells and lead to light-induced effects (see Sections 6 and 11)

As shown in Table I, several other techniques have been used to make a-Si : H solar cells, but the efficiencies are all rather low (S4.0%) However, some of these approaches are relatively new, and further optimization will undoubtedly lead to higher efficiencies ’The sputter deposition of a-Si : H is described by Moustakas in Volume 2 1 A, Chapter 4 Sputtered a-Si : H films appear to contain more defects than glow-di scharge-produced films (Vik- torovitch et al., 198 l), possibly as a result of more bombardment damage or the inclusion of Ar in the growing film

The formation of a-Si : H films by the chemical vapor deposition (CVD)

10 D E CARLSON

of higher silanes is covered by Hirose and Scott in Volume 2 1 A, Chapters 6

and 7 In general, CVD techniques involve slow deposition rates or long

posthydrogenation treatments in order to make a-Si : H films of reasonable

quality

111 Relevant Material Properties

1 OPTICAL ABSORPTION

Efficient solar energy conversion requires that the photovoltaic material

be capable of absorbing a significant fraction of the energy in sunlight As

shown in Fig 1, the absorption coefficient of undoped a-Si : H is greater than

lo4 cm-1 over most of the visible light region (- 1.9 eV < hv < -4.0 eV)

Thus, an a-Si : H film need be only - 1 pm thick to absorb most of the solar

energy

As described in Volume 2 1 B, “Hydrogenated Amorphous Silicon: Opti-

cal Properties,” the absorption coefficient of undoped a-Si : H is strongly

influenced by the deposition conditions For example, the optical gap

usually increases as the substrate temperature decreases, and this effect has

been attributed to an increase in the hydrogen content (Zanzucchi et al.,

hv (eV)

FIG 1 The optical absorption coefficient as a function of photon energy for undoped

a-Si : H (solid curve), ptype a-Si : H (dashed curve), and ptype a-Si : C: H (dashed-dotted

curve) Both ptype films contains a few atomic percent of boron, and the a-Si : C : H film also

contains -20 at % of carbon

11

2 SOLAR CELLS

1977) The optical properties of a-Si : H appear to be directly influenced by the alloying effect of hydrogen and the nature of the hydrogen bonding Cody et al (198 1) have presented evidence that in some cases the optical properties are determined by structural disorder, which is influenced indi- rectly by the presence of hydrogen through it!; ability to relieve strain In any event, changing the optical properties of a-Si : H by varying the deposition conditions also changes the electronic properties The data shown in Fig 1 for undoped a-Si : H represent device quality iaaterial made under optimum deposition conditions (diffusion length r 0.5 pm)

As described in Part IV, high performance a-Si : H solar cells are usually made in a p-i-n configuration so that some light is also absorbed in the

doped layers Since the carrier lifetime in doped layers is usually very short, most of the light absorbed in these layers is lost to recombination For boron-doped a-Si : H, the absorption coefficient is generally much larger than that for intrinsic or undoped a-Si : H (see Fig 1 ), so that - 20% of the

useful light may be lost by absorption in the p layer (- 10 nm thick) of a

p-i-n cell (Carlson, 1980b) This absorption loss can be reduced signifi-

cantly by alloying the p layer with carbon (Pmkove, 1978) as shown in Fig

1 Another approach is to alloy the doped layers with nitrogen since it also increases the optical gap (Kurata et al., 198 I ) , but a-Si : N : H layers have not yet led to high-performance devices The optical absorption in the doped layers can also be reduced by using microcrystalline Si : H layers (Carlson and Smith, 1982)

For stacked junction solar cells, one wcluld like to tailor the optical properties so that the active material in the first junction has a wide band gap, and the active layers in other junctions have progressively narrower band gaps (see Section 8) As mentioned earlier, either carbon or nitrogen alloying can be used to open the optical gap, while alloying with tin or germanium can reduce the optical gap Representative optical data for undoped a-Si : C : H and a-Si : Ge : H films are shown in Fig 2

lifetime product ( p ~ ) greater than lo-' cin2 V-' using the expression

In most a-Si:H solar cells, a built-in electric field (F) assists in the collection of photogenerated carriers, and efficient collection occurs as long

as the drift length ( , m F ) is significantly larger than the film thickness Crandall ( 1982) has shown that the transporf in p- i- n cells can be charac-

/d = (kTpT/q)'f2

FIG 2 The optical absorption coefficient as a function of photon energy for a-Si:H

(Eopt= 1.73 eV), a-Si,,,8Geo,8z:H (Eopt = 1.3 eV) (von Roedern ef al., 1982), and a-Sio,,,C0,,,: H (Eop, = 2.0 eV) (Morimoto ef al., 1982)

terized by a collection length f, = (p,,~,, + pprp)F that is the sum of the electron and hole drift lengths In high performance cells, the collection length is typically 5 5 pm in the short-circuit mode The collection length decreases as the cell goes into forward bias, and transport via diffusion dominates as the cell approaches the open-circuit condition

Diffusion lengths on the order of 1 pm have been measured in undoped a-Si : H by using the constant surface photovoltage technique (see Chapter 7

by Moore in Volume 21C) and similar values have been inferred by Faughnan et af (1983) from measurements of the drift length Even larger

diffusion lengths can be inferred from the measurements of Komuro et af

(1983), who used two interfering lasers to create a transient grating of photogenerated camers and then measured the decay rate with a probe laser They were able to measure camer lifetimes in the range of 3 - 5 psec Lifetimes in the range of 10- 30 psec have been measured by the junction recovery technique for injection current densities of - 10 mA cm-2 (Snell et af., 1981) These lifetimes imply mobilities in the range of

10-I- cm2 V-' sec-l for material with a diffusion length of - I pm

2 SOLAR CELLS 13

Hall effect measurements indicate mobilities of - lo-' cmz V-I sec-' for

both electrons (Dresner, 1980) and holes (Dresner, 1983) Tiedje et al

(198 1) have measured drift mobilities of - 1 cmz V-' for electrons and

- lo-' cmz V-I sec-I for holes However, Silver et al (1982) have esti-

mated that the electron mobility is 2 100 cm2 V-I sec-' by using the

reverse recovery technique

Although there is some question about the values ofp and 7 , it is clear that the product of pu'5 is on the order of lo-' cmz V-' in good-quality a-Si : H, and thus photogenerated camers can be efficiently collected

3 DENSITY OF GAP STATES

Large diffusion lengths can only be obtained in a-Si : H material that

possesses a low density of gap states (See Chapter 2 by Cohen of Volume

2 1C for detailed information on the measurements of the density of states in a-Si : H.) The principal recombination center in a-Si : H is a silicon dangling

bond that in the neutral state can trap either electrons or holes (Street, 1982)

Some dangling bonds are created during the growth of the films due to hydrogen out-diffusion (Fritzsche et al., 1978) Others appear to be asso-

ciated with microstructural imperfections such as polymer chains (Knights

et al., 1979) or with impurities such as oxygen (Pontuschka et al., 1982) and

carbon (Morimoto er al., 1982)

The defect level associated with the neutral dangling bond appears to be located - 1 O- 1.25 eV below the conduction band edge with the singly charged negative state, -0.25-0.45 eV higher (Morigaki et al., 1982; Jack-

son, 1982) In crystalline silicon, the neutral state of the divacancy is 0.8 1 eV below the conduction-band edge, and the correlation energy for adding an

electron is +0.25 eV These values are in rough agreement considering the

wider band gap of a-Si : H (- 1.6 - 1.8 eV) as compared to crystalline silicon

4 IMPURITIES

As mentioned earlier, impurities can create defect levels in the gap of a-Si: H The most common impurities are oxygen, carbon, and nitrogen, with concentrations typically in the range of 10l8- lozo cm-' (Magee and

14 D E CARLSON

Carlson, 1980) The source of oxygen may be either an air leak, outgassing of H,O, COY or CO, from walls of the vacuum system, or contaminants such as (SiH,),O (disiloxane) in the SiH, cylinder Nitrogen may also come from either an air leak, outgassing from walls, or N, in the SiH, cylinder The source of carbon may be either outgassing of CO and/or CO, , or hydrocar- bons that originate primarily from pump oils

The effects of impurities on solar cells have been investigated by deliber- ately adding gases such as H,O, N, , and CH, to the SiH, discharge during the deposition of the a-Si: H (Carlson, 1977c, 1982a) Cell efficiency was reduced by - 15 - 30% by adding either - 0.2% H,O or - 1% N, or - 10%

CH, to the SiH, discharge Delahoy and Griffith (1 98 1) found that the presence of both oxygen and nitrogen in the SiH, causes a greater reduction

in solar-cell efficiency than that caused by the presence of either gas by itself This synergistic effect suggests that some of the recombination centers are nitrogen - oxygen complexes, and defects such as NO, have been observed

by electron spin resonance in x-irradiated a-Si : H films (Pontuschka et al.,

1982)

In addition to siloxanes and nitrogen, other contaminants that have been detected in SiH, cylinders are monochlorosilane (SiH,Cl) (Delahoy and Griffith, 1981) and tetrahydrofuran (C,H,O) (A Gallagher and J Scott, unpublished results, 1982) Delahoy and Griffith (1981) showed that the solar-cell performance was seriously degraded by the presence of - 500 ppm

of C1 in the a-Si : H material They also showed that small quantities of phosphine (- 10 ppm) in SiH, could drastically reduce device performance However, small quantities of diborane (a few parts per million) in SiH, often improve the conversion efficiency of a-Si : H solar cells due to compensation

of donorlike impurities (Carlson, 1980c; Haruki et al., 1983)

Work at RCA has shown that impurities such as oxygen, carbon, nitro- gen, and chlorine can reduce the diffusion length (&) in a-Si : H (Carlson et

al., 1983a) As shown in Table 11, significant reductions are caused by

- 0.2% disiloxane or - 2% nitrogen in SiH, Both contaminants also cause a large increase in the space-charge density in the dark leading to small depletion widths ( W,) Compositional analyses of these films showed that the first one contained -0.4 at % oxygen and the second, -0.5 at %

nitrogen The addition of - 2% methane to the SiH, discharge (- 0.6 at %

carbon in the film) causes both Id and W, to decrease by about 40% Adding

0.07% dichlorosilane (- 40-ppm C1 in the film) causes a similar reduction in

1, but does not significantly affect W,

The disorder inherent in hydrogenated amorphous silicon gives rise to tails in the density of state distribution near the band edges Calculations by

2 SOLAR CELLS 15

TABLE I1 EFFECTS OF IMPURITIES ON DIFFUSION LENGTHS

Impurity concentrations ( ~ m - ~ ) Discharge

atmosphere ld (pm) W, (pm) O(X 1019) C(X 1019) N(X 1019) CI(X 10”)

Microstructural imperfections such as polymer chains, clustered hydro- gen, and microvoids can adversely affect the electronic properties of a-Si : H Dangling bonds are often associated with these microstructural defects probably as a result of weaker Si - H bonds than are found in highdensity, bulk a-Si : H, where distributed monohydnde bonding dominates (Reimer

et al., 1981) Under certain deposition conditions (e.g., low substrate tem- peratures, Ar dilution, high power), the a-Si: H films may grow with a

columnar morphology in which (SiH2), groups are associated with the connective material between the columns (Knights et al., 1979)

The morphology and density of a-Si : H vary with the deposition condi- tions, and generally the films become more dense as the substrate tempera- ture is increased (DAntonio and Konnert, 198 11) Under certain deposition conditions, even films grown at relatively high substrate temperatures

(-330°C) can be porous and exhibit properties that change with time (Carlson ef al., 1979/1980)

The transport in a-Si : H may be strongly in!tluenced by the presence of

16 D E CARLSON

inhomogenities that give rise to potential fluctuations (Overhof and Beyer,

198 1) The model predicts a thermally activated mobility and roughly accounts for the Meyer- Neldel behavior (a,, = a, exp(-E,/kT) where

In o, E,) The inhomogenities may be compositional variations due to

microvoids or hydrogen clustering

6 METASTABLE STATES

Staebler and Wronski (1977) were the first to observe light-induced changes in the properties of a-Si : H The Staebler- Wronski effect is now known to affect the performance of a-Si : H solar cells through the creation

of recombination centers and charged traps (Carlson er af., 1983b) These light-induced centers are metastable and can be annealed out at tempera- tures of - 150-200°C

The light-induced creation of recombination centers causes the diffusion length to decrease with exposure time as shown in Fig 3 (Carlson et al.,

1984b) The diffusion length was measured by the surface photovoltage method (Dresner er al., 1980), and similar results were obtained from an analysis of device characteristics (Faughnan er af., 1983)

Some of the metastable centers have been associated with impurities such

as oxygen (Crandall, 1981) and carbon (Crandall et af., 1983) Deep-level transient spectroscopy (DLTS) has been used to identify a center associated with oxygen that has a characteristic activation energy of - I .O eV, whereas

(- 100 mW cm-2) Most devicequality films exhibit behavior intermediate to the curves shown here

2 SOLAR CELLS 17

.4 eV

START

OF PEAK ASSOCIATED

E, zs 1.OeV

*./' .-•

.*

TIME ( s e c ) FIG 4 Capacitance transient DLTS signal for a p - n junction at T = 437°K containing 10

at % carbon in the p layer [From Crandall ef al (1983).]

that associated with carbon has an activation energy of - 0.4 eV Figure 4

shows that the transient voltage signals from these two centers are clearly distinguishable because of their different response times

Other metastable centers appear to be associated with microstructural imperfections since light-induced effects are influenced by annealing treat- ments (Staebler and Pankove, 1980) and by variiitions in deposition condi- tions (Carlson, 1982b; Hirabayashi et al., 1982) For a more thorough discussion of metastable effects see Chapter 1 1 by Schade of Volume 2 1 B

There are two mechanisms that limit the built-In potential in a-Si : H solar cells One is the existence of band-tail states as mentioned earlier, and the other is the low doping efficiency of a-Si : H Spear and LeComber (1976)

18 D E CARLSON

used conductivity and field-effect measurements to estimate that - 30% of the phosphorus incorporated in a-Si : H was electronically active as shallow donors Using photoemission, von Roedern et al (1979) determined that

- 10% of the phosphorus and boron in a-Si : H is active as donors and acceptors, respectively LeComber et al ( 1980) estimated doping efficien-

cies of -0.5% for a-Si : H that had been ion implanted with boron and

- 0.2% for phosphorus-implanted a-Si : H

More recently, Faughnan and Hanak ( 1983) have used spectral response

data to determine that the concentration of acceptors is - lOI9 cm-3 for

p-type a-Si : H layers containing - lo2' boron atoms (as determined by SIMS) for a doping efficiency of - 1% Dresner ( 1983) has estimated that the

doping efficiency of boron in a-Si : H is - 0.1 % for films containing between

1019 and lo2' boron atoms ~ m - ~ Thus, more recent estimates of the doping

efficiency are in the range 0.1 - 1 .O% Apparently, many of the dopant atoms

do not go into electronically active substitutional sites

Street er al (198 1 ) have shown that doping a-Si: H with boron or phos-

phorus creates new defect states that are in some cases associated with dangling bonds Other defects produced by doping appear to be associated with dopant- hydrogen complexes (Carlson et al., 1982) Nuclear magnetic

resonance studies have shown that nearly all the boron in p-type a-Si : H is threefold coordinated in either Si3B or Si,BH configurations (Greenbaum et

gap of undoped a-Si : H is typically about 1.7 eV, the built-in potential of

a-Si: H p- i-n solar cells is about 1.0 eV (Williams et al., 1979) Improving

the conductivity of the doped layers should lead to larger built-in potentials and consequently higher conversion efficiencies The conductivity can be increased significantly by forming microcrystalline-doped Si : H films (Mat- suda et al., 1980), but since these films contain both amorphous and

crystalline phases, there is no significant increase in the built-in potential (Carlson and Smith, 1982)

The built-in potential of a-Si:H p-i-n cells has been increased by

alloying the p layer with carbon (Tawada et al., 1982) However, as shown in

Fig 5, the resistivity of the p layer increases as the optical gap (or carbon content) increases Thus, the carbon alloying is decreasing the doping efficiency in this case The increase in V, with increasing carbon content of the p layer is apparently associated with a suppression of the dark current by the wide-band-gap p layer

/ /

/

/

/ /

Q

/ / / @

1982) The p layer typically contains about 20-30 at % carbon (Morimoto

2 SOLAR CELLS 21

et al., 1982) and has an optical gap of -2.0 eV (Tawada et al., 1982) Generally, the p and n layers contain on the order of 1 at % boron or phosphorus, respectively The Sn02 layer may be chosen to be -60 nm thick so that it acts as an antireflection layer or it may be much thicker so

that the sheet resistance is low (- 1 - 10 Q/U) Silver can be used as a back metal contact so that most of the unabsorbed light reaching the back contact

is reflected back into the i layer However, either A1 or Ti (- 5 - 10 nm)/Al are more practical metal contacts that are alijo relatively reflective

Another structure that has been used to make relatively efficient a-Si : H solar cells is shown in Fig 6b In this case, the p layer is deposited on a steel substrate, and indium tin oxide (ITO) is electron-beam evaporated onto the n-layer The I T 0 serves as both a top contact layer and an antireflection coating The steel substrate may be coated with Cr to improve the back surface reflection Generally, in all p- i- n cdls the top doped layer is thin

(- 10 nm) in order to minimize losses due to absorption and recombination

in that layer

The stacked junction structure is fabricated by growing one p-i-n

junction directly on top of another (see Fig '7) Ideally, one wants to adjust the band gaps of the i layers so that each layer produces the same photocur- rent and the device efficiency is maximized Thus, the first p- i- n junction would employ a wide-band-gap layer (e.g., 1.9 eV) and the second junction would have a much smaller band gap (e.g., 1.1 eV) The stacked junction structure can be extended to three or more junctions where the band gap progressively decreases toward the back of the cell The band gaps can be tailored by using alloys such as a-Si : C : H and a-Si : Ge : H (see Section 1)

Since the junctions are in series, the voltages are additive The doped layers must be relatively thin (- 10 nm) to avoid significant absorption and recom- bination losses in those layers, and they must also be relatively conducting

so that the n - p junctions are effectively shorted because of tunneling There are other structures that have been used to make a-Si : H solar cells such as Schottky-barrier and MIS configurations, but since the conversion efficiencies are generally less than 696, we will not discuss these structures here (for more information on these structures, see Carlson, 1982b)

9 SOLAR-CELL PERFORMANCE

The principal method of characterizing solar-cell performance is the measurement of conversion efficiency while the cell is exposed to 1 sun illumination (- 100 mW cm-2) The conversion efficiency is determined by measuring the current - voltage characteristic (see Fig 8), locating the maxi-

mum power point (P, = J,V,), and also measuring the solar insolation

1 = 10.196, area = 1.09 cm2 V, = 0.84 V, J , = 1.78 mA cm-2, FF = 0.676, illumination =

98.62 mW cm-2, T = 25.7"C [From Catalano et al., Attainment of 10% conversion efficiency

in amorphous silicon solar cells Con/: Rec IEEE Photovoltaic Spec Con/: Vol 16, 01982

IEEE.]

(Pi) The conversion efficiency is then given by

where J, is the short-circuit current density, V, the open-circuit voltage, and FF the fill factor as defined by Eq (1)

The I- V characteristic shown in Fig 8 is for a cell with the structure

glass/SnO,/p- i-n/Ag, where the p layer is alloyed with carbon (Catalano et

al., 1982) The conversion efficiency was 10.1% with V,=O.84 V,

J, = 17.8 mA ern-,, and FF = 0.676 The spectral response (or external

quantum efficiency) of the same 10.1% cell is shown in Fig 9 An integra-

tion of the quantum efficiency with the AM l solar spectrum gave a current

density of 17.6 mA ern-,, in good agreement with the measured value of J,

(Catalano et al., 1982)

The performance characteristics of a variety of different types of a-Si : H solar cells are listed in Table 111 The last structure listed is actually a hybrid configuration where the a-Si : H cell is stacked on top of a crystalline silicon cell (Hamakawa et al., 1983)

Since the current density of a solar cell in the dark obeys the relation

J = J,[exp(qV/nkT) - 11, (2)

FIG 9 Quantum efficiency as a function of wavelen,ph for a p - i - n cell with q = 10.1%

[From Catalan0 et al Attainment of 10% conversion efficiency in amorphous silicon solar

cells Conf: Rec IEEE Photovoltaic Spec Cord, Vol 16, 01982 IEEE.]

one can also characterize a cell by its reverse situration current density (Jo)

and its diode quality factor (n) Relatively efficient p-i-n cells ( q > 7%) typically exhibit values of Jo in the range 1O-Iz- lo-'' A cm-Z and diode quality factors of - 1.5 - 1.8 A diode quality factor under illumination (n')

can be determined from the expression

(3) and for good p - i - n cells, n = 1 O

The performance of a p - i- n cell as a function of temperature is shown in Fig 10 (G Swartz, private communication, 1982) The solar-cell structure is glass/SnO,/p- i- n/Ti/Al, where the p layer is alloyed with carbon From

room temperature to 65"C, l/q (dq/dT) = -0.0032 "C-' as V, fell from 0.764 V to 0.630 V; J, increased from 1 1.75 mA cm-z to 12.15 mA cm-z, and FF increased from 0.662 to 0.678 As the temperature increased beyond

65"C, l/q (dq/dT) = -0.0072 "C-I while& leveled off at - 12.2 mA cm-2 and the fill factor started decreasing

Han et al (1982) studied the temperature dependence of p-i-n cells deposited on steel using the structure shown in Fig 6b For temperatures ranging from 25 to IOOT, they found the conversion efficiency to be relatively constant Although V, decreased with increasing temperature

(dV,/dT= -2.67 mV OC-l), it was compensated by the increase in J,

These cells exhibited values of Jo = 3 X 10" A cm-z, n = 2, and n1 = 1.2

V , = (nlkT/q) ln(J,/J0) + 1

10 MODELING O F SOLAR-CELL OPERATION

There have been a number of theoretical papers that model the operation

of a-Si : H solar cells by starting with Poisson's equation, the continuity